PHILADELPHIA (AP) — Ask Americans how race relations have changed under their first black president and they are ready with answers.

Ashley Ray, a white woman, hears more people debating racial issues. “I know a lot of people who really thought we were OK as a nation, a culture, and now they understand that we’re not,” she says.

Karl Douglass, a black man, sees stereotypes easing. “White people deal with me and my family differently,” he says.

Jose Lozano, who is Hispanic by way of Puerto Rico, believes prejudice is emerging from the shadows. “Now the racism is coming out,” he says.

In the afterglow of Barack Obama’s historic victory, most people in the United States believed that race relations would improve. Nearly four years later, has that dream come true? Americans have no shortage of thoughtful opinions, and no consensus.

As the nation moves toward the multiracial future heralded by this son of an African father and white mother, the events of Obama’s first term, and what people make of them, help trace the racial arc of his presidency.

Shortly before the 2008 election, 56 percent of Americans surveyed by the Gallup organization said that race relations would improve if Obama were elected. One day after his victory, 70 percent said race relations would improve and only 10 percent predicted they would get worse.

Just weeks after taking office, Obama said, “There was justifiable pride on the part of the country that we had taken a step to move us beyond some of the searing legacies of racial discrimination.”

Then he joked, “But that lasted about a day.”

Or, rather, three months.

By July 2009, the black Harvard professor Henry Louis Gates was arrested for yelling at a white police officer who questioned whether Gates had broken into his own home. Asked to comment, Obama said he didn’t know all the facts, but Gates was a personal friend and the officer had acted “stupidly.”

The uproar was immediate. Obama acknowledged afterward, “I could’ve calibrated those words differently.”

Ed Cattaneo, a retired computer training manager from Cape May, N.J., points to that episode as evidence of how Obama has hurt race relations.

“He’s made them terrible,” says Cattaneo, who is white. He also sees Obama as siding against white people through actions such as his Justice Department’s decision to drop voter intimidation charges against New Black Panthers and in a program to turn out the black vote called “African-Americans for Obama.”

Larry Sharkey, also white, draws different conclusions from the past four years.

“Attitudes are much better,” Sharkey says as he slices raw meat in a Philadelphia butcher shop. He remembers welcoming a black family that moved next door to him 20 years ago in Claymont, Del. A white neighbor advised him not to associate with the new arrivals, warning, “Your property values are going to go down.”

That kind of thing would never happen today, Sharkey says.

As Obama dealt with fallout from the Gates affair during the summer of 2009, the tea party coalesced out of opposition to Obama’s stimulus and health care proposals. The vast majority of tea partyers were white. A small number of them displayed racist signs or were connected to white supremacist groups, prompting the question: Are Obama’s opponents motivated by dislike of the president’s policies, his race — or both?

As that debate grew, Obama retreated to the race-neutral stance that has been a hallmark of his career. An October 2009 Gallup poll showed a large drop in racial optimism since the election, with 41 percent of respondents saying that race relations had improved under Obama. Thirty-five percent said there was no change and 22 percent said race relations were worse.

The president has discussed race in occasional speeches to groups such as the National Urban League or the National Council of La Raza, and in interviews with Hispanic and African-American media outlets. But he usually walks a careful line, allowing the nation to get used to the idea of a black president without doing things to make race seem a central aspect of his governance.

“There is a totally different psychological frame of reference that this country has never had,” says William Smith, executive director of the National Center for Race Amity at Wheelock College.

He cites evidence of progress from the mindset of children in his programs to new history curriculums in Deep South schools.

“To me, that’s a quantum leap,” Smith says.